ThmUniversalClassNotCardinal (3.67, Theorem): Class of all sets is not a cardinal class

Standalone kernel entity record from 3. Set/Class-Theoretic Foundations (3.01–3.78) — View in Complete Entity Database (#ThmUniversalClassNotCardinal) →

Formula Display:
Proof Trees:

ThmUniversalClassNotCardinal (3.67) — Class of all sets is not a cardinal class

Morse-Kelley / Von Neumann-Bernays-Gödel class comprehension, sethood, ordinals, Dunaev pairs, cardinals, universes, and reflection.

Num Entity Database Record (Vertical Field Table)
3.67
Title Class of all sets is not a cardinal class #ThmUniversalClassNotCardinal #label-class-of-all-sets-is-not-a-cardinal-class
Classification Theorem
Formula
0(¬Card(V))
0\(\href{../symbols/delimiters-brackets.html}{(} \href{../symbols/neg-conn.html}{\neg} \href{../symbols/card-pred.html}{\mathrm{Card}} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/universal-class-const.html}{\mathbf{V}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST TpCard
Scheme of Types 0(¬Card(V))
Verification Verified (Kernel) · Standalone Entry (ThmUniversalClassNotCardinal) → · (3.67) · #ThmUniversalClassNotCardinal